> But what if we take two random choices (2-random) and just use LRU between those two choices?
> Also, we can see that pseudo 3-random is substantially better than pseudo 2-random, which indicates that k-random is probably an improvement over 2-random for the k. Some k-random policy might be an improvement over DIP.
This sounds very similar to tournament selection schemes in evolutionary algorithms. You can control the amount of selective pressure by adjusting the tournament size.
I think the biggest advantage here is performance. A 1v1 tournament is extremely cheap to run. You don't need to maintain a total global ordering of anything.